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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 12 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 12 Maths Textbook Solution.

Answers (1)

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Answer: \lambda=8

Hint: Here, we use the basic concept of Algebra

Given:

A=\begin{bmatrix} 1 & 1\\ 1 & 1 \end{bmatrix}

A^{^{4}}=\lambda A

Solution:

A^{^{4}}= A^{2}\times A^{2}

A^{2}=\begin{bmatrix} 1 & 1\\ 1 & 1 \end{bmatrix}\times \begin{bmatrix} 1 & 1\\ 1 & 1 \end{bmatrix}

A^{2}=\begin{bmatrix} 1 +1& 1+1\\ 1+1 & 1+1 \end{bmatrix}=\begin{bmatrix} 2 & 2\\ 2 & 2 \end{bmatrix}

A^{2}\times A^{2}=\begin{bmatrix} 2 & 2\\ 2 & 2 \end{bmatrix}\begin{bmatrix} 2 & 2\\ 2 & 2 \end{bmatrix}

=\begin{bmatrix} 4+4 & 4+4\\ 4+4 & 4+4 \end{bmatrix}=\begin{bmatrix} 8 & 8\\ 8 & 8 \end{bmatrix}

A^{4}=\begin{bmatrix} 8 & 8\\ 8 & 8 \end{bmatrix}

A^{^{4}}=\lambda A

\begin{bmatrix} 8 & 8\\ 8 & 8 \end{bmatrix}=\lambda \begin{bmatrix} 1 & 1\\ 1 & 1 \end{bmatrix}

\begin{bmatrix} 8 & 8\\ 8 & 8 \end{bmatrix}= \begin{bmatrix} \lambda & \lambda\\ \lambda & \lambda \end{bmatrix}

So,\lambda=8

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